Aitchison Embeddings for Learning Compositional Graph Representations

TL;DR

This paper introduces a novel graph embedding method based on Aitchison geometry, producing interpretable node representations as mixtures that reflect archetypal factors, with competitive performance and explainability.

Contribution

It proposes a compositional graph embedding framework using Aitchison geometry and ILR coordinates, enabling interpretable and coherent representations of graph nodes.

Findings

Achieves competitive performance on node classification and link prediction tasks.

Provides inherently interpretable embeddings reflecting archetypal trade-offs.

Enables principled component restriction via subcompositional coherence.

Abstract

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to graph structure. Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors. Motivated by this structure, we propose a compositional graph embedding framework grounded in Aitchison geometry, the canonical geometry for comparing mixtures. Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction; we consider both fixed and learnable ILR bases. Across node classification and link prediction, our method achieves competitive performance with strong baselines while providing explainability by construction rather than post-hoc. Finally, subcompositional coherence enables principled component restriction: removing and renormalizing subsets preserves a well-defined geometry, which we exploit via subcompositional dimensionality removal to probe how archetype groups influence representations and predictions.